Physics GRE Discussion Forums

An electron with energy E and momentum kh/2pi is incident from the left on a potential
step of height V > E at x = 0 . For x > 0 , the space part of the electron’s
wave function has the form
(A) e^ikx (B) e^ik'x; k'< k (C) e^-a x , where a is real and positive
(D) sinkx (E) identically zero

the answer given is C. but this is true only for bound state. what if it is a scattering state? then the answer should be A.
how to know about when they are asking for bound or scattering state?

Since E<V you have only bound states and no scattering states. Furthermore, the wave function must me finite and go to zero as the distance from the "wall" increases. Hence, answer C is the correct answer.
Answer A is a traveling wave which is the case for E>V.